Debye Temperature

Debye temperature

[də′bī ′tem·prə·chər] (solid-state physics) The temperature θ arising in the computation of the Debye specific heat, defined by k θ = h ν, where k is the Boltzmann constant, h is Planck's constant, and ν is the Debye frequency. Also known as characteristic temperature.

Debye Temperature

a physical constant of matter that characterizes numerous properties of solids, such as specific heat, electric conductivity, thermal conductivity, broadening

Table 1
Metal	θ_p	Semiconducto	θ_D	Dielectric	θ_o
Hg...............	60–90...............	Sn (gray)...............	212	AgBr	150
Pb...............	94.5...............	Ge...............	366	NaCI	320
Na...............	160...............	Si...............	658	Diamond	1,850
Ag...............	225...............
W...............	270...............
Cu...............	339...............
Fe...............	467...............
Be...............	1,160...............

of X-ray spectral lines, and elastic properties. The concept was first introduced by P. Debye in his theory of specific heat. The Debye temperature is defined by the equation

θ_D = h v_D/k

where k is Boltzmann’s constant, h is Planck’s constant, and v_D is the maximum frequency of the vibrations of a solid’s atoms. The Debye temperature indicates the approximate temperature limit below which quantum effects may be observed. At temperatures T ≫ θ_D the specific heat of a crystal consisting of atoms of one type at constant volume is C_r = 6 cal (^°C. mole)^-1, which agrees with Dulong and Petit’s law. At T ≪ θ_D the specific heat is proportional to (Γ/θ_p,)³ (the Debye T³ approximation).

Typical values of the Debye temperature for some substances are given in degrees Kelvin in Table 1.